Lesson Worksheet: Approximating Radicals Mathematics • 8th Grade

In this worksheet, we will practice approximating the square or cube root of a number and then using it to solve real-world problems.

Q1:

Daniel is trying to find which two whole numbers lie on either side of 51. He decides that it will be helpful to use what he has been taught about square numbers.

What is the greatest square number below 51?

What is the smallest square number above 51?

Hence, determine the two consecutive whole numbers that 51 lies between.

  • A6 and 9
  • B8 and 9
  • C7 and 9
  • D7 and 8
  • E6 and 8

Q2:

By considering square numbers, determine an approximation for 83 to the nearest whole number.

Q3:

Which of the integers below is the closest to 353?

  • A17
  • B6
  • C18
  • D7

Q4:

Daniel wants to find an approximation for 2 accurate to two decimal places. He sets up the equation 𝑥=2 and then starts using trial and improvement to find the solution as seen in the table.

𝑥𝑥=2big/small
11=1s
22=4b
1.51.5=2.25b
1.41.4=1.96s
1.41
1.42
1.415

Determine the value of 1.41 giving your answer accurate to three decimal places.

Determine the value of 1.42 giving your answer accurate to three decimal places.

Determine the value of 1.415 giving your answer accurate to three decimal places.

Hence, what is the value of 2 accurate to two decimal places?

Q5:

Which of the following is the correct construction of 2+34 on a number line by using a compass and a straightedge?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following is the correct construction of 13 on a number line using a compass and a straightedge?

  • A
  • B
  • C
  • D
  • E

Q7:

Without using a calculator, find two consecutive integers that 13+6 lies between.

  • A5, 6
  • B6, 7
  • C7, 8
  • D4, 5

Q8:

Solve (𝑥2)=6, then approximate your answer to one decimal place.

Q9:

A flashlight emits a light beam whose width 𝑤 at a distance of 𝑑 is given by 𝑤=1.2𝑑. Determine, to the nearest tenth, the width of the beam 26 feet away from the flashlight.

Q10:

Which of the following numbers is closest to 5?

  • A106
  • B8
  • C24
  • D94
  • E120

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